any arrangement of the orange dots so that the mean
and median are correct

The median is the middle number. In other words there
are always as many points to the right of the median
as to the left.

Try dragging the points so that half of them are to
the left of MEDIAN and half of them
are to the right of MEDIAN.
The two points in the middle should be the same
distance from MEDIAN.
The middle point should be at
MEDIAN.

As long as there are as many points to the left and to
the right of the median, the median will stay the same.
But the arithmetic mean is calculated using the value
of every point. Try moving the points on either side
of the median closer and further from the median to
see how the mean is affected.

There are a number of different ways to arrange the
points so the mean is MEAN and the median is
MEDIAN.